Question

When Lydia goes bowling, her scores are normally distributed with a mean of 150 and a standard deviation of 12. Out of the 60 games that she bowled last year, how many of them would she be expected to score between 127 and 157, to the nearest whole number?​

Answer 1

39 games

Explanation:

To answer this question, we can use the empirical rule, which states that for a normal distribution, about 68% of the data values are within one standard deviation of the mean, about 95% are within two standard deviations, and about 99.7% are within three standard deviations. In this case, the mean is 150 and the standard deviation is 12, so one standard deviation below the mean is 150 - 12 = 138, and one standard deviation above the mean is 150 + 12 = 162. The interval from 127 to 157 is slightly smaller than one standard deviation on either side of the mean, so we can estimate that about 65% of the data values are within this interval. To find the number of games that Lydia would be expected to score between 127 and 157, we can multiply 65% by the total number of games, which is 60. This gives us 0.65 x 60 = 39. Rounding to the nearest whole number, we get 39 games.

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